{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<small>\n",
    "Copyright (c) 2017 Andrew Glassner\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n",
    "</small>\n",
    "\n",
    "\n",
    "\n",
    "# Deep Learning From Basics to Practice\n",
    "## by Andrew Glassner, https://dlbasics.com, http://glassner.com\n",
    "------\n",
    "## Chapter 19: Optimizers\n",
    "### Notebook 2: Accuracy in splitting a 1D data set\n",
    "\n",
    "This notebook is provided as a “behind-the-scenes” look at code used to make some of the figures in this chapter. It is still in the hacked-together form used to develop the figures, and is only lightly commented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import gridspec\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "import seaborn as sbn; sbn.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Make a File_Helper for saving and loading files.\n",
    "\n",
    "save_files = True\n",
    "\n",
    "import os, sys, inspect\n",
    "current_dir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n",
    "sys.path.insert(0, os.path.dirname(current_dir)) # path to parent dir\n",
    "from DLBasics_Utilities import File_Helper\n",
    "file_helper = File_Helper(save_files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "matplotlib.rcParams['axes.titlesize'] = 14\n",
    "matplotlib.rcParams['axes.labelsize'] = 14\n",
    "matplotlib.rcParams['axes.labelpad'] = 8\n",
    "matplotlib.rcParams['xtick.labelsize'] = 14\n",
    "matplotlib.rcParams['ytick.labelsize'] = 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_dot_data(points_per_side = 20):\n",
    "    np.random.seed(42)\n",
    "    left_data = np.random.uniform(-5, -.01, size=points_per_side)\n",
    "    right_data = np.random.uniform(-.01, 5, size=points_per_side)\n",
    "    dot_X = np.ravel([left_data, right_data])\n",
    "    dot_y = np.ravel([[0]*points_per_side, [1]*points_per_side])\n",
    "    return (dot_X, dot_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_dot_data(ax, dot_X, dot_y, y_val):  \n",
    "    cm = LinearSegmentedColormap.from_list('mymap', ['#1C5BA8', '#D6A234'])\n",
    "    xmin = np.min(dot_X) - 1\n",
    "    xmax = np.max(dot_X) + 1\n",
    "    ax.plot([xmin, xmax], [y_val, y_val], color='black', linewidth=1, zorder=10)\n",
    "    ax.scatter(dot_X, [y_val]*len(dot_X), c=dot_y, s=80, cmap=cm, zorder=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_dot_data_figure(dot_X, dot_y):\n",
    "    plt.figure(figsize=(8,1))\n",
    "    ax = plt.gca()\n",
    "    draw_dot_data(ax, dot_X, dot_y, 0)\n",
    "    plt.xlim(np.min(dot_X)-.5, np.max(dot_X)+.5)\n",
    "    plt.yticks([],[])\n",
    "    file_helper.save_figure('dot-data')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAB9CAYAAAAyXtLNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAIUQQgghYsz/B6DlTClLyS83AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cf40b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(dot_X, dot_y) = make_dot_data(points_per_side = 40)\n",
    "draw_dot_data_figure(dot_X, dot_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# this filter throws a warning about a library incompatibility, but it works\n",
    "from scipy.signal import savgol_filter\n",
    "\n",
    "def draw_dot_data_curve(ax, dot_X, dot_y, smooth=False):\n",
    "    val_list = np.linspace(np.min(dot_X)-1, np.max(dot_X)+1, 200)\n",
    "    yvals = []\n",
    "    for v in val_list:\n",
    "        total_error = 0\n",
    "        for x,y in zip(dot_X, dot_y):\n",
    "            if ((x < v) and (y == 1)) or ((x > v) and (y == 0)):\n",
    "                    total_error += 1\n",
    "        yvals.append(total_error)\n",
    "    yrange = (np.min(yvals), np.max(yvals))\n",
    "    if smooth:\n",
    "        yvals = savgol_filter(yvals, 51, 3) # window size 51, polynomial order 3\n",
    "    yvals = np.interp(yvals, (np.min(yvals), np.max(yvals)), (0,1))\n",
    "    ax.plot(val_list, yvals)\n",
    "    return yrange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_dot_data_and_curve(dot_X, dot_y, smooth=False):\n",
    "    ax = plt.gca()\n",
    "    (ymin, ymax) = draw_dot_data_curve(ax, dot_X, dot_y, smooth)\n",
    "    plt.ylim(-.5, 1.1)\n",
    "    draw_dot_data(ax, dot_X, dot_y, -.25)\n",
    "    plt.xlim(np.min(dot_X)-.5, np.max(dot_X)+.5)\n",
    "    plt.yticks([0, 1.1],(ymin, ymax))\n",
    "    plt.ylabel('error')\n",
    "    plt.xlabel('dividing point position')\n",
    "    file_helper.save_figure('dot-data-and-curve-smooth-'+str(smooth))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAAIACAYAAABgsr9NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrxBCCCGE8Gv/Dynj26XQWXQUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cf408d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_dot_data_and_curve(dot_X, dot_y, smooth=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.5/lib/python3.5/site-packages/scipy/linalg/basic.py:1018: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  warnings.warn(mesg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAAIACAYAAABgsr9NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMmlMeImIiIjIpDHhJSIiIiKT9j9GYwnmdgcinQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105e80668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_dot_data_and_curve(dot_X, dot_y, smooth=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
